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At least 73 records · Page 4

Liquid Interfacial Electron Microscopy Identifies Nanogalvanic Corrosion in Pearlitic Steel

The nanoscale mechanisms of localized corrosion in low carbon steels have remained elusive due to the complexity of studying the degradative material behavior at nanoscale solid-liquid interfaces. We identified various steps in the nanogalvanic corrosion processes using in-situ liquid-cell scanning transmission electron microscopy (STEM) using a microfluidic holder by Hummingbird Scientific. Initial work, performed at low magnification, identified the initiation point on a 1018 low-carbon steel surface. This initiation point was determined to be a triple junction of two ferrite grains bridging a cementite grain in contact with a baseline electrolyte of 6 uM CO2 dissolved in a buffered (2.78 uM Na2SO4) aqueous solution, pH 6.1. The pre-etched low-carbon steel surface was prepared using focused ion beam lift-out procedures to extract a cross-section of the low-carbon steel surface, which then was thinned to about 150 nm and transferred to a SiN membrane microfluidic window. The transfer was made using a lift-out needle to attach the low-carbon steel lamella to the corner of the SiN window, and then Pt/C deposition held the lamella in contact with the window while it was released from the lift out needle. To identify the triple point on the low carbon steel lamella, prior to attachment on the SiN window, the sample was characterized for compositional variations with energy dispersive x-ray spectroscopy mapping, grain orientation and phase mapping with precession electron diffraction, and thickness mapping with energy filtered transmission electron microscopy. This pre-characterization prior to the in-situ experiment provided a map of the multiphase and multigrain structure, where the in-situ liquid cell imaging provided a clear understanding of the initiation point on the sample. These data were cross-correlated to paint a holistic picture of the triple junction site, enabling low electron-fluence in-situ snapshot imaging to avoid dominating the native corrosion reactions with effects from the incident electron beam. This initial result identified that localized, nanogalvanic corrosion at the phase interface was the dominant corrosion process in the low-carbon steel, so we next targeted the observation of an array of these nanogalvanic features phase boundaries in a pearlite grain. Near-surface ferrite/cementite phase interfaces that typify pearlitic low-carbon steel were extracted, pre-characterized, and imaged for the in-situ corrosion processes. The sample was a cross-section from a pearlite grain, with alternating ferrite and cementite grains that extended microns down from the pre-etched low-carbon steel pipe surface. After contact with a buffered aqueous solution, the phase boundaries between the ferrite and cementite began to dissolve, with observable material loss and thickness changes in the dark-field and bright-field STEM images. Within minutes, the corrosion front proceeded deeper into the material, claiming a thin layer of ferrite around all exposed phase boundaries before progressing laterally into the ferrite matrix, converting the ferrite to corrosion product normal to each buried cementite grain. Formation of the corrosion product causes a volumetric expansion, creating a lateral wedging force that mechanically ejects the cementite grains from their grooves and leaves behind percolation channels into the steel substructure. Rapid and deleterious, this nanogalvanic corrosion pathway represents an important target for understanding and preventing run-away degradation in this common building material. Observation of this corrosion mechanism was enabled by the combination of pre-characterization using standard structural, grain, and compositional analysis in the TEM, which provides maps for understanding the reaction propagation captured in low-dose, in-situ, liquid-cell STEM.

corrosion↗

Phase-Insensitive Ultrasonic Testing System

Ultrasonic testing system developed for use in revealing hidden disbonds at rough, inaccessible interfaces between layers of material. Includes array of small piezoelectric transducers, receiving outputs electronically processed individually and combined in such way as to make system phase-insensitive, overcoming limitations imposed by phase-sensitivity. Development of present ultrasonic system and phase-insensitive-array technique which based motivated by need to detect disbonds under conditions of bondline inhibitor, liner, and fuel at ends of segments of solid rocket motor of space shuttle. Here, liner-to-fuel bondline very rough with respect to ultrasonic wavelength.

Madaras, Eric I.↗

Phase 2 of the Array Automated Assembly Task for the Low Cost Solar Array Project

Two process specifications supplied by contractors were tested. The aluminum silk screening process resulted in cells comparable to those from sputtered Al. The electroless plating of contacts specification could be used only with extensive modification. Several experiments suggest that there is some degradation of the front junction during the Al back surface field (BSF) fabrication. A revised process sequence was defined which incorporates Al BSF formation. A cost analysis of this process yielded a selling price of $0.75/watt peak in 1980.

Campbell, R. B.↗

Phase 2 of the array automated assembly task for the low cost solar array project

The process sequence for the fabrication of dendritic web silicon into solar panels was modified to include aluminum back surface field formation. Plasma etching was found to be a feasible technique for pre-diffusion cleaning of the web. Several contacting systems were studied. The total plated Pd-Ni system was not compatible with the process sequence; however, the evaporated TiPd-electroplated Cu system was shown stable under life testing. Ultrasonic bonding parameters were determined for various interconnect and contact metals but the yield of the process was not sufficiently high to use for module fabrication at this time. Over 400 solar cells were fabricated according to the modified sequence. No sub-process incompatibility was seen. These cells were used to fabricate four demonstration modules. A cost analysis of the modified process sequence resulted in a selling price of $0.75/peak watt.

Campbell, R. B.↗

NASA Tech Briefs, November 2008

Topics covered include: Digital Phase Meter for a Laser Heterodyne Interferometer; Vision System Measures Motions of Robot and External Objects; Advanced Precipitation Radar Antenna to Measure Rainfall From Space; Wide-Band Radar for Measuring Thickness of Sea Ice; Vertical Isolation for Photodiodes in CMOS Imagers; Wide-Band Microwave Receivers Using Photonic Processing; L-Band Transmit/Receive Module for Phase-Stable Array Antennas; Microwave Power Combiner/Switch Utilizing a Faraday Rotator; Compact Low-Loss Planar Magic-T; Using Pipelined XNOR Logic to Reduce SEU Risks in State Machines; Quasi-Optical Transmission Line for 94-GHz Radar; Next Generation Flight Controller Trainer System; Converting from DDOR SASF to APF; Converting from CVF to AAF; Documenting AUTOGEN and APGEN Model Files; Sequence History Update Tool; Extraction and Analysis of Display Data; MRO DKF Post-Processing Tool; Rig Diagnostic Tools; MRO Sequence Checking Tool; Science Activity Planner for the MER Mission; UAVSAR Flight-Planning System; Templates for Deposition of Microscopic Pointed Structures; Adjustable Membrane Mirrors Incorporating G-Elastomers; Hall-Effect Thruster Utilizing Bismuth as Propellant; High-Temperature Crystal-Growth Cartridge Tubes Made by VPS; Quench Crucibles Reinforced with Metal; Deep-Sea Hydrothermal-Vent Sampler; Mars Rocket Propulsion System; Two-Stage Passive Vibration Isolator; Improved Thermal Design of a Compression Mold; Enhanced Pseudo-Waypoint Guidance for Spacecraft Maneuvers; Altimetry Using GPS-Reflection/Occultation Interferometry; Thermally Driven Josephson Effect; Perturbation Effects on a Supercritical C7H16/N2 Mixing Layer; Gold Nanoparticle Labels Amplify Ellipsometric Signals; Phase Matching of Diverse Modes in a WGM Resonator; WGM Resonators for Terahertz-to-Optical Frequency Conversion; Determining Concentration of Nanoparticles from Ellipsometry; Microwave-to-Optical Conversion in WGM Resonators; Four-Pass Coupler for Laser-Diode-Pumped Solid-State Laser; Low-Resolution Raman-Spectroscopy Combustion Thermometry; Temperature Sensors Based on WGM Optical Resonators; Varying the Divergence of Multiple Parallel Laser Beams; Efficient Algorithm for Rectangular Spiral Search; Algorithm-Based Fault Tolerance Integrated with Replication; Targeting and Localization for Mars Rover Operations; Terrain-Adaptive Navigation Architecture; Self-Adjusting Hash Tables for Embedded Flight Applications; Schema for Spacecraft-Command Dictionary; Combined GMSK Communications and PN Ranging; System-Level Integration of Mass Memory; Network-Attached Solid-State Recorder Architecture; Method of Cross-Linking Aerogels Using a One-Pot Reaction Scheme; An Efficient Reachability Analysis Algorithm.

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Velocity-space Origins of the Pressure–Strain Interaction in Multipopulation Distributions and Its Application to Magnetic Reconnection

A forefront research question is how energy evolves in weakly collisional plasmas for which departures from local thermodynamic equilibrium (LTE) are significant. The standard approach is studying the terms in the non-LTE energy evolution equation derived by taking the second moment of the Boltzmann equation, but the resultant fluid metrics do not retain information about which particles at which velocities drive energy evolution. A widely studied channel for internal energy density evolution is the pressure–strain interaction. Here, we employ the kinetic pressure–strain, a phase-space diagnostic whose velocity-space integral recovers the pressure–strain interaction to disambiguate the contributions to the pressure–strain interaction from disparate particle populations in composite phase-space densities. We develop phase-space analogs of the pressure–strain interaction decompositions to provide the phase-space origins of normal versus sheared flow. We introduce the “kinetic strain-rate” tensor, the phase-space analog of the strain-rate tensor, which we argue is needed to interpret the phase-space origins of the pressure–strain interaction. To demonstrate the utility of these quantities, we investigate them for composite electron distributions near the electron diffusion region in two-dimensional particle-in-cell simulations of antiparallel symmetric magnetic reconnection. We find that the phase-space-based diagnostics isolate the roles of distinct populations. These results contribute to a growing body of work providing new methods for quantifying phase-space energy evolution for a broad array of processes, from magnetic reconnection to collisionless shocks and turbulence, opening new pathways for answering longstanding problems of particle energization in weakly collisional plasmas.

79 ASTRONOMY AND ASTROPHYSICS↗

Large-Area Periodic Arrays of Atomically Flat Single-Crystal Gold Nanotriangles Formed Directly on Substrate Surfaces

The advancement of nanoenabled wafer-based devices requires the establishment of core competencies related to the deterministic positioning of nanometric building blocks over large areas. Within this realm, plasmonic single-crystal gold nanotriangles represent one of the most attractive nanoscale components but where the formation of addressable arrays at scale has heretofore proven impracticable. In this work, a benchtop process is presented for the formation of large-area periodic arrays of gold nanotriangles. The devised growth pathway sees the formation of an array of defect-laden seeds using lithographic and vapor-phase assembly processes followed by their placement in a growth solution promoting planar growth and threefold symmetric side-faceting. The nanotriangles formed in this high-yield synthesis distinguish themselves in that they are epitaxially aligned with the underlying substrate, grown to thicknesses that are not readily obtainable in colloidal syntheses, and present atomically flat pristine surfaces exhibiting gold atoms with a close-packed structure. As such, they express crisp and unambiguous plasmonic modes and form photoactive surfaces with highly tunable and readily modeled plasmon resonances. The devised methods, hence, advance the integration of single-crystal gold nanotriangles into device platforms and provide an overall fabrication strategy that is adaptable to other nanomaterials.

42 ENGINEERING↗

Time delay and integration array (TDI) using charge transfer device technology. Phase 2, volume 1: Technical

The 20x9 TDI array was developed to meet the LANDSAT Thematic Mapper Requirements. This array is based upon a self-aligned, transparent gate, buried channel process. The process features: (1) buried channel, four phase, overlapping gate CCD's for high transfer efficiency without fat zero; (2) self-aligned transistors to minimize clock feedthrough and parasitic capacitance; and (3) transparent tin oxide electrode for high quantum efficiency with front surface irradiation. The requirements placed on the array and the performance achieved are summarized. This data is the result of flat field measurements only, no imaging or dynamic target measurements were made during this program. Measurements were performed with two different test stands. The bench test equipment fabricated for this program operated at the 8 micro sec line time and employed simple sampling of the gated MOSFET output video signal. The second stand employed Correlated Doubled Sampling (CDS) and operated at 79.2 micro sec line time.

Source record↗

Theory of a Traveling Wave Feed for a Planar Slot Array Antenna

Planar arrays of waveguide-fed slots have been employed in many radar and remote sensing applications. Such arrays are designed in the standing wave configuration because of high efficiency. Traveling wave arrays can produce greater bandwidth at the expense of efficiency due to power loss in the load or loads. Traveling wave planar slot arrays may be designed with a long feed waveguide consisting of centered-inclined coupling slots. The feed waveguide is terminated in a matched load, and the element spacing in the feed waveguide is chosen to produce a beam squinted from the broadside. The traveling wave planar slot array consists of a long feed waveguide containing resonant-centered inclined coupling slots in the broad wall, coupling power into an array of stacked radiating waveguides orthogonal to it. The radiating waveguides consist of longitudinal offset radiating slots in a standing wave configuration. For the traveling wave feed of a planar slot array, one has to design the tilt angle and length of each coupling slot such that the amplitude and phase of excitation of each radiating waveguide are close to the desired values. The coupling slot spacing is chosen for an appropriate beam squint. Scattering matrix parameters of resonant coupling slots are used in the design process to produce appropriate excitations of radiating waveguides with constraints placed only on amplitudes. Since the radiating slots in each radiating waveguide are designed to produce a certain total admittance, the scattering (S) matrix of each coupling slot is reduced to a 2x2 matrix. Elements of each 2x2 S-matrix and the amount of coupling into the corresponding radiating waveguide are expressed in terms of the element S11. S matrices are converted into transmission (T) matrices, and the T matrices are multiplied to cascade the coupling slots and waveguide sections, starting from the load end and proceeding towards the source. While the use of non-resonant coupling slots may provide an additional degree of freedom in the design, resonant coupling slots simplify the design process. The amplitude of the wave going to the load is set at unity. The S11 parameter, r of the coupling slot closest to the load, is assigned an arbitrary value. A larger value of r will reduce the power dissipated in the load while increasing the reflection coefficient at the input port. It is now possible to obtain the excitation of the radiating waveguide closest to the load and the coefficients of the wave incident and reflected at the input port of this coupling slot. The next coupling slot parameter, r , is chosen to realize the excitation of that radiating waveguide. One continues this process moving towards the source, until all the coupling slot parameters r and hence the S11 parameter of the 4-port coupler, r, are known for each coupling slot. The goal is to produce the desired array aperture distribution in the feed direction. From an interpolation of the computed moment method data for the slot parameters, all the coupling slot tilt angles and lengths are obtained. From the excitations of the radiating waveguides computed from the coupling values, radiating slot parameters may be obtained so as to attain the desired total normalized slot admittances. This process yields the radiating slot parameters, offsets, and lengths. The design is repeated by choosing different values of r for the last coupling slot until the percentage of power dissipated in the load and the input reflection coefficient values are satisfactory. Numerical results computed for the radiation pattern, the tilt angles and lengths of coupling slots, and excitation phases of the radiating waveguides, are presented for an array with uniform amplitude excitation. The design process has been validated using computer simulations. This design procedure is valid for non-uniform amplitude excitations as well.

Rengarajan, Sembiam↗

Array automated assembly task, phase 2. Low cost silicon solar array project

Several modifications instituted in the wafer surface preparation process served to significantly reduce the process cost to 1.55 cents per peak watt in 1975 cents. Performance verification tests of a laser scanning system showed a limited capability to detect hidden cracks or defects, but with potential equipment modifications this cost effective system could be rendered suitable for applications. Installation of electroless nickel plating system was completed along with an optimization of the wafer plating process. The solder coating and flux removal process verification test was completed. An optimum temperature range of 500-550 C was found to produce uniform solder coating with the restriction that a modified dipping procedure is utilized. Finally, the construction of the spray-on dopant equipment was completed.

Rhee, S. S.↗

Phase aligner for the Electronically Scanned Thinned Array Radiometer (ESTAR) instrument

A prototype Phase Aligner (PA) or the Electronically Scanned Thinned Array Radiometer instrument has been designed and tested. Implemented in a single Xilinx XC3042PC84-125 Field Programmable Gate Array (FPGA), it is a dual-port register file which allows independent storage and phase coherent retrieval of antenna array data by the Central Processing Unit (CPU). It has dimensions of 4 x 20 bits and can be used at clock frequencies as high as 25 MHz. The ESTAR is a passive synthetic-aperture radiometer designed to sense soil moisture and ocean salinity at L-band.

Chren, William A., Jr.↗

Weak-signal Phase Calibration Strategies for Large DSN Arrays

The NASA Deep Space Network (DSN) is studying arrays of large numbers of small, mass-produced radio antennas as a cost-effective way to increase downlink sensitivity and data rates for future missions. An important issue for the operation of large arrays is the accuracy with which signals from hundreds of small antennas can be combined. This is particularly true at Ka band (32 GHz) where atmospheric phase variations can be large and rapidly changing. A number of algorithms exist to correct the phases of signals from individual antennas in the case where a spacecraft signal provides a useful signal-to-noise ratio (SNR) on time scales shorter than the atmospheric coherence time. However, for very weak spacecraft signals it will be necessary to rely on background natural radio sources to maintain array phasing. Very weak signals could result from a spacecraft emergency or by design, such as direct-to-Earth data transmissions from distant planetary atmospheric or surface probes using only low gain antennas. This paper considers the parameter space where external real-time phase calibration will be necessary, and what this requires in terms of array configuration and signal processing. The inherent limitations of this technique are also discussed.

interferometry↗

Planetary Radar Imaging with the Deep-Space Network's 34 Meter Uplink Array

A coherent uplink array consisting of up to three 34-meter antennas of NASA's Deep Space Network has been developed for the primary purpose of increasing EIRP at the spacecraft. Greater EIRP ensures greater reach, higher uplink data rates for command and configuration control, as well as improved search and recovery capabilities during spacecraft emergencies. It has been conjectured that Doppler-delay radar imaging of lunar targets can be extended to planetary imaging, where the long baseline of the uplink array can provide greater resolution than a single antenna, as well as potentially higher EIRP. However, due to the well known R-4 loss in radar links, imaging of distant planets is a very challenging endeavor, requiring accurate phasing of the Uplink Array antennas, cryogenically cooled low-noise receiver amplifiers, and sophisticated processing of the received data to extract the weak echoes characteristic of planetary radar. This article describes experiments currently under way to image the planets Mercury and Venus, highlights improvements in equipment and techniques, and presents planetary images obtained to date with two 34 meter antennas configured as a coherently phased Uplink Array.

imaging↗

Planetary Radar Imaging with the Deep-Space Network's 34 Meter Uplink Array

A coherent Uplink Array consisting of two or three 34-meter antennas of NASA's Deep Space Network has been developed for the primary purpose of increasing EIRP at the spacecraft. Greater EIRP ensures greater reach, higher uplink data rates for command and configuration control, as well as improved search and recovery capabilities during spacecraft emergencies. It has been conjectured that Doppler-delay radar imaging of lunar targets can be extended to planetary imaging, where the long baseline of the uplink array can provide greater resolution than a single antenna, as well as potentially higher EIRP. However, due to the well known R4 loss in radar links, imaging of distant planets is a very challenging endeavor, requiring accurate phasing of the Uplink Array antennas, cryogenically cooled low-noise receiver amplifiers, and sophisticated processing of the received data to extract the weak echoes characteristic of planetary radar. This article describes experiments currently under way to image the planets Mercury and Venus, highlights improvements in equipment and techniques, and presents planetary images obtained to date with two 34 meter antennas configured as a coherently phased Uplink Array.

uplink array↗

Space-Based Telemetry and Range Safety Project Ku-Band and Ka-Band Phased Array Antenna

The National Aeronautics and Space Administration Space-Based Telemetry and Range Safety study is a multiphase project to increase data rates and flexibility and decrease costs by using space-based communications assets for telemetry during launches and landings. Phase 1 used standard S-band antennas with the Tracking and Data Relay Satellite System to obtain a baseline performance. The selection process and available resources for Phase 2 resulted in a Ku-band phased array antenna system. Several development efforts are under way for a Ka-band phased array antenna system for Phase 3. Each phase includes test flights to demonstrate performance and capabilities. Successful completion of this project will result in a set of communications requirements for the next generation of launch vehicles.

Whiteman, Donald E.↗

Acoustic Phased Array Quantification of Quiet Technology Demonstrator 3 Advanced Inlet Liner Noise Component

Acoustic phased array flyover noise measurements were acquired as part of the Boeing 737 MAX-7 NASA Advanced Inlet Liner segment of the Quiet Technology Demonstrator 3 (QTD3) flight test program. This paper reports on the processes used for separating and quantifying the engine inlet, exhaust and airframe noise source components and provides sample phased array-based comparisons of the component noise source levels associated with the inlet liner treatment configurations. Full scale flyover noise testing of NASA advanced inlet liners was conducted as part of the Quiet Technology Demonstrator 3 flight test program in July and August of 2018. Details on the inlet designs and testing are provided in the companion paper of Reference 1. The present paper provides supplemental details relating to the acoustic phased array portion of the analyses provided in Ref. 1. In brief, the test article was a Boeing 737MAX-7 aircraft with a modified right hand (starboard side) engine inlet, which consisted of either a production inlet liner, a NASA designed inlet liner or a simulated hard wall configuration (accomplished by applying speed tape over the inlet acoustic treatment areas). In all three configurations, the engine forward fan case acoustic panel was replaced with a unperforated (hardwall) panel. No other modifications to any other acoustic treatment areas were made. The left hand (port side) engine was a production engine and was flown at idle thrust for all measurements in order to isolate the effects of the inlet liners to the right hand engine. As described in Ref. 1, the NASA inlet treatment consists of laterally cut slots (cut perpendicular to the flow direction) which are designed to reduce excrescence drag while maintaining or exceeding the liner acoustic noise reduction capabilities. The NASA inlet liner consists of a Multi-Degree of Freedom (MDOF) design with two breathable septum layers inserted into each honeycomb cell [1]. The aircraft noise measurements were acquired for both takeoff (flaps 1 setting, gear up) and approach (flaps 30 gear up and gear down) configurations. The inlet and flight test configurations are summarized in Table 1. Table 1: Inlet Treatment and Flight Configurations Inlet Forward Fan Case Aircraft Production Hardwall Flaps 1, gear up; flaps 30 gear up; flaps 30 gear down NASA Hardwall Flaps 1, gear up; flaps 30 gear up; flaps 30 gear down Hardwall Hardwall Flaps 1, gear up; flaps 30 gear up; flaps 30 gear down III.Test Description and Hardware The flight testing was conducted at the Grant County airport in Moses Lake, WA, between 27 July and 6 August 2018. The noise measurement instrumentation included 8 flush dish microphones arranged in a noise certification configuration as well as an 840 microphone phased array. The flush dish microphones were used to quantify the levels and differences in levels between the various inlet treatments. The phased array was used to separate and quantify the narrowband (tonal) and broadband noise component levels from the engine inlet/exhaust and from the airframe. Phased array extraction of the broadband component was critical to this study because it allowed for the separation of the inlet component from the total airplane level noise even when it was significantly below the total level. Figure 1 provides an overview of the phased array microphone layout as well as a detailed image of an individual phased array microphone mounted in a plate holder (the microphone sensor is the dot in the center of the plate). The ground plane ensemble array microphones (referred to as “ensemble array” in this paper) were mounted in plates with “flower petal” edges designed to minimize edge scattering effects. Fig. 1 Flyover test microphone layout. The phased array configuration was the result of a progressive development of concepts originally implemented in Ref. 2 and refined over the following years, consisting namely of multiple multi-arm logarithmic spiral subarrays designed to cover overlapping frequency ranges and optimized for various aircraft emission angles. For the present case, the signals from all 840 microphones were acquired on a single system. The 840 microphones were parsed into 11 primary subarray sets spanning from smallest to largest aperture size and labeled accordingly as “a, b, …, k”, where “a” corresponds to the smallest fielded subarray and “k” corresponds to the largest aperture subarray. The apertures ranged from approximately 10 ft to 427 ft in size (in the flight direction) with the subarrays consisting of between 215 and 312 microphones. Figure 2 shows three such subarrays, k, h and a. As done in Ref. 2, microphones were shared between subarrays in order to reduce total channel count. Fig. 2 Sample subarray sizes (20° from overhead – refer to Figure 3a discussion). In addition to the above, each of the 11 primary subarray sets consisted of four subarrays optimized to provide near equivalent array spatial resolution in both the flight and lateral directions within 30 degrees of overhead (i.e., airplane directly above the center of the array), namely, at angles  of 0, ±10, ±20 and ±30 degrees relative to overhead where angle  is defined as shown in Figure 3a. This allowed for optimized aircraft noise measurements from 60 to 120 degree emission angle.6 An example of this pletharray design is shown in Figure 3b for the k subarray. When the aircraft is at overhead, the microphones indicated by the blue markers are used for beamforming. When the aircraft is at angles ±10 degrees from overhead, both the blue and red colored microphones are used, and so on for the ±20 and ±30 degree aircraft locations. See Ref. 3 for extensive details on pletharray design for aeroacoustic phased array testing. 6 In the discussions that follow, emission angle values are used. These are the angles at the time sound is emitted relative to the engine axis and are calculated based on flight path angle, body aircraft body angle with respect to the relative wind direction, and engine axis angle relative to aircraft body angle.

Brusniak, Leon↗